1. Reading Vernier Scales MS&T Physics 1135 and 2135 Labs

2. Vernier Scales: Background  Invented in 1631 by Pierre Vernier, Vernier scales allow very accurate measurement of lengths and angles through the use of two scales.  One scale (the primary or data scale) provides the base measurement, with the other (the secondary, indicating, or Vernier scale) increasing precision.  The reading on the Vernier scale is added to the reading on the primary scale to increase the precision. A typical Vernier adds one or two significant figures to a given measurement.  In Physics 1135 and 2135 labs, we use three main devices with Vernier scales: calipers, torsion lathes, and spectrometers. Each is covered in turn in the following slides. MS&T Physics 1135 and 2135 Labs: Reading Vernier ScalesSlide 2/6

3. Measurement Basics: the Meterstick  A typical meterstick with divisions spaced 1 mm apart is accurate give or take a millimeter. In this example, x = 33 ± 1 mm  To increase precision, we could add more lines, which would be very difficult to read.  Next, we’ll measure the same object with calipers to see how Vernier scales circumvent this obstacle. MS&T Physics 1135 and 2135 Labs: Reading Vernier ScalesSlide 3/6

4. Vernier Calipers  The base measurement is given by the primary marking just left of the zero on the Vernier (green arrow): 3.3 cm, or 33 mm  Next, find the Vernier marking that best aligns with a primary marking (red arrow): the 9th division.  Our measurement is 33 + 9*0.02 mm, or 33.18 mm  This is accurate give or take one division: x = 33.18 ± 0.02 mm MS&T Physics 1135 and 2135 Labs: Reading Vernier ScalesSlide 4/6

5. Vernier Scale on a Torsion Lathe  Our torsion lathes use a Vernier to measure angles.  The outer rim is marked in degrees, and there are ten divisions on the Vernier.  Thus, this device is accurate to ±0.1°  The reading shown is 9.2 ± 0.1° MS&T Physics 1135 and 2135 Labs: Reading Vernier ScalesSlide 5/6

6. Vernier Scale on a Spectrometer  Our spectrometers also use a Vernier to measure angles.  The outer ring is marked in half- degrees, and there are 30 divisions on the Vernier. This divides 1° into 60 increments, so this device is accurate to ±(1/60)°, or ±1 minute of arc.  The reading shown is 245.5 + 12/60° or 245.7° MS&T Physics 1135 and 2135 Labs: Reading Vernier ScalesSlide 6/6